This appendix contains a proofs of the results in the main text and further analysis on the two FIM estimators ˆI1(θ)and ˆI2(θ). In particular, Appendix C presents an analysis of how the FIM estimators and their covariance tensors change under reparametrization. Appendix D presents element-wise bound alternatives to those presented in Section 3.2. Appendix E explores various results using alternative norms to the Frobenius norm results of the main text. Appendix F presents an analysis on taking a linear combination of the two FIM estimators.

A fundamental structural model for data is that the data points lie close to an unknown subspace, meaning that the matrix created by concatenating the data vectors has low rank. We address a particular low-rank matrix recovery problem where we wish to recover a set of vectors from a low-dimensional subspace after they have been individually compressed (or "sketched").